CONCLUSIONS.
The conclusions to be drawn from the foregoing discussion may be briefly
stated as follows:
First. That the codex in its present form is composite, being made up
from two or more different original manuscripts, as Dr. Foerstemann has
suggested.
Second. That a number of minor changes and additions have been made by a
subsequent hand, possibly after it had assumed its present form.
Third. That the year referred to in the larger series is one of 360 days;
also, that in instances of this kind the count is continuous, and hence
not consistent with the generally received idea of the Maya calendar, in
which, the four year series forms a necessary part of the system, unless
some other method of accounting for the five supplemental days can be
discovered than that which has hitherto been accepted.
Fourth. On the other hand, indications of the four year series are
certainly found in all of the Maya manuscripts; for example, in Plates
25-28 of the Dresden Codex and Plates XX-XXIII of the Manuscript
Troano,[339-1] which seem to be based on this series; in fact, the
numbers attached to the days in the latter can be accounted for in no
other way. Plates 3-6 of the Cortesian Codex are apparently based upon
the same system. The numbers in the loops on Plates 71, 72, and 73,
Dresden Codex, heretofore alluded to and represented in Fig. 371,
apparently defy explanation on any supposition except that they refer to
the numbers of the ahaues, which are based upon the four year
series.[339-2] The frequent occurrence in connection and in proper order
of both the first and the terminal days of the year apparently refers to
the same system. Many of the quadruple series no doubt relate to the four
cardinal points and the four seasons; yet there are some which cannot be
explained on this theory alone.
It is impossible, therefore, to exclude this system from consideration in
studying the chronology of the codices, although there are a number of
the numerical series of the Dresden manuscript which cannot be made to
fit into it on any hypothesis so far suggested. The same thing is also
found to be true in regard to some, in fact most, of the series found in
the Mexican manuscripts. This confusion probably arises in part from the
apparently well established fact that two methods of counting time
prevailed among both Mexicans and Mayas: one, the solar year in ordinary
use among the people, which may be termed the vulgar or common calendar;
the other, the religious calendar used by the priests alone in arranging
their feasts and ceremonies, in which the cycle of 260 days was taken as
the basis. But this supposition will not suffice as an explanation of
some of the long series of the Dresden Codex, in which the year of 360
days appears to have been taken as a unit of measure, unless we
assume--as Foerstemann seems to have done--that what have been taken as
years are simply high units and counting the whole as so many days, refer
the sum to the cycle of 260 days, which will in almost every case measure
them evenly as a whole, or by its leading factor, 13. That the smaller
series attached to day columns are all multiples of 13 and referable to
the cycle of 260 days has been shown by Foerstemann as well as in the
preceding part of this paper. But it is worthy of note that the
difficulty mentioned occurs only in reference to series found in that
portion of the Dresden manuscript which Foerstemann has designated Codex B
(page 24 being considered as belonging thereto).
The red unit number symbol, with a circle of dots around it, seen
occasionally in the Manuscript Troano, seems to have some connection with
the four year series. Take, for example, the one in the lowest division
of Plate VII.
The series commences in the lower right hand corner of Plate VIII, where
the day column with which it is connected is found. The days of this
column, reading downward, are as follows: Ahau, Eb, Kan, Cib, Lamat, and
the number over them is I, but without any dots around it, while the
terminal I of the series is inclosed in the circle of dots. What is the
meaning of this marked distinction? It is evident that it is something
which does not apply equally to all the days of the columns; yet, as it
is the terminal number, it must relate to some one of them. If we examine
the series carefully I think the reason for the distinction will be
explained; Written out in full, it is as follows:
I.
Ahau
Eb }
Kan } 10, XI; 10, VIII; 10, V; 10, II; 12[?], [(I)].
Cib
Lamat
The last black number is 10 in Brasseur's fac simile, but should be 12.
Making this correction, the series is regular and of the usual form. The
sum of the black numbers is 52, which is the interval between the days,
and the number over the column is the same as the final red number.
If we turn now to the calendar (Table II) and select Ahau of the Kan
column, and 1, the seventeenth number of the eighth figure column, and
count 52 days, we reach 1 Eb, the second day of our column as given
above; 52 days more bring us to 1 Kan, the first day of the first month
in the calendar and third day of our column. If the theory of the four
year series be correct, then 1 Kan of the Kan series must be the first
day of the first year of an Indication or week of years. This fact was
probably considered by the aboriginal artist of sufficient importance to
give this day a mark of distinction. As it is not possible for any of the
other days of the column to be thus distinguished, it is fair to presume
this peculiar marking of the final number refers to Kan. Moreover, this
distinction would not occur if any other than the Kan series were used.
In the upper division of Plate IX of the same manuscript is the following
series:
XIII
Men }
Manik } 20, VII; 20 [(I)]; 1, II; 4, VI; 7, XIII.
Cauac }
Chuen
Akbal
In this, I, the second red number of the series, has the circle of dots
around it. The number over the column is partially obliterated, but is
readily restored, and should be XIII.
If we select, on our calendar, the Cauac column, or series, a reason for
this distinction will appear. The sum of the black numbers is 53, which
is also the interval between the days. As has heretofore been shown, the
red numbers of the series refer to certain days selected by the priests,
for special reasons unknown to us, which occur between the days of the
column.
In this case the intermediate days are as follows:
Between 13 Manik and 13 Cauac: 7 Manik, 1 Manik, 2 Lamat, and 6 Eb.
Between 13 Cauac and 13 Chuen: 7 Cauac, 1 Cauac, 2 Ahau, and 6 Kan.
Here we find the explanation for which we are seeking, as in the interval
between 13 Cauac and 13 Chuen is 1 Cauac, which, if the Cauac column of
the calendar be selected, is the first day of the year 1 Cauac, the first
year of an Indication. As this occurs only when a year commencing with
Cauac is selected, we infer that the series is based upon the system with
the four year series.
The best illustration of this peculiarity and the strongest evidence of
its signification is probably found in the series contained in the middle
division, Plate XI, same manuscript. This, when written out and the
numbers properly arranged, is as follows:
[(I)] [(I)]
Oc Ahau }
Cib Cimi } 1, II; 2, IV; 2, VI; 5, XI; 2, XIII; 4, IV; 9(?) [(I)].
Ik Eb }
Lamat Ezanab
Ix Kan
The last black number of the series is 9, but should be 10 to render the
series complete. Making this correction, the series is of the usual type;
the sum of the black numerals is 26, the interval between the days of
the columns is 26, and the final red numeral is the same as that over the
columns.
As the circle of dots is around the final red number and also around each
of those over the columns, the distinction indicated must refer to one or
more days of each column.
As the last days only of the columns are year bearers, the mark of
distinction probably applies to them. Selecting for the left hand column
the Ix series of years and commencing with 1 Oc, the seventeenth day of
the eighth month, we count 26 days. This brings us to 1 Cib, the third
day of the tenth month, or tenth figure column of our calendar and second
day of the first day column of the series; 26 days more to 1 Ik; 26 more
to 1 Lamat, and 26 more to 1 Ix, the first day of the year 1 Ix, which,
according to the four year series, will be the first year of an
Indication. Selecting the Kan series for the second column and counting
in the same way from 1 Ahau, the seventeenth day of the eighth month, or
eighth figure column of the calendar, the last day is found to be 1 Kan,
the first day of the year 1 Kan, which must also be the first year of an
Indication.
Unit numerals marked in this manner are found in two or three places in
the Cortesian Codex, but there is none in the Dresden Codex. The series
with which they are connected in the former, except that in the middle
division of Plate 24, are too much obliterated to be traced throughout.
This, by making two slight and apparently authorized corrections, is as
follows:
[(I)]
Cimi }
Ezanab } 11, XII(?); 11, X; 6, III; 8, XI; 7(?), V; 9, I.
Oc }
Ik
Ix
The first red numeral of the line is X in the original and the next to
the last black number is 6. By changing the former to XII and the latter
to 7 the sum of the series will be 52, which is the interval between the
days of the column.
Using the Ix column in the calendar and commencing with 1 Cimi, counting
as heretofore, the last day of the column of the series is found to be 1
Ix, the first day of the year 1 Ix and the first year of an Indication,
according to the four year system.
A somewhat remarkable confirmation of the theory here advanced is
presented in a series found in the middle division of Plate II of the
Manuscript Troano.
The series, when written out with the substitutes heretofore used, is as
follows:
[(I)] [(I)]
Manik Ymix }
Men (?) Been } 9, X; 6, III; 11, I.
Chuen Chicchan }
Akbal Caban
Men Muluc
In Brasseur's fac simile the second symbol of the left hand column is
clearly that for Men. If this be accepted as correct, then no year bearer
(Kan, Muluc, Ix, Cauac) would be found in either column and the theory we
have advanced regarding the signification of the dots around the red unit
over the column would fall to the ground. Nor is this the only difficulty
we meet with in attempting to apply the theory to this series. The sum of
the black numbers is 26, which should also be the interval between the
days of the columns. Counting 26 days from 1 Manik brings us to 1 Been
instead of 1 Men; 26 more to 1 Cauac, a day not found in either column as
given in the original. Taking the second column and counting 26 days from
1 Ymix, we reach 1 Manik, instead of 1 Been. This gives us the key to the
series and solves the riddle. We must commence with 1 Ymix, then take 1
Manik, then 1 Been, and so on, going alternately from column to column.
Adopting this method and using the Cauac column of our calendar, Table
II, the result is as follows: Commencing with 1 Ymix, the third day of
the tenth figure column, and counting 26 days, we reach 1 Manik; 26 days
more bring us to 1 Been, and 26 more to 1 Cauac, the first day of the
first year of an Indication. The 1 Men of the left hand column should
therefore be 1 Cauac, which is also proved by counting the intervals,
without regard to the week numbers. For example, from Ymix to Been is 12
days, from Been to Chicchan 12 days, from Manik to Cauac 12 days, and so
on through each column. Or, if we take the columns alternately, the
interval is six days, thus: From Ymix to Manik, 6 days; from Manik to
Been, 6 days; from Been to Cauac, 6 days; from Cauac to Chuen, 6 days,
and so on to the end.
Although the proof is not absolutely conclusive that these red unit
numerals have this mark of distinction for the reason given, it
nevertheless furnishes what would seem to be a satisfactory explanation,
and, if so, affords proof that the calendar system, based upon the four
year series, was in vogue when the Manuscript Troano and the Codex
Cortesianus were written.
This mark of distinction is found in a strange and unusual relation in
the lower division of Plate XV, Manuscript Troano. The first red numeral
of the series is given thus:
[Illustration: FIG. 372. Numeral character from the lower division of
Plate XV, Manuscript Troano.]
Most of the day and about half of the numeral symbols are obliterated,
but all that are necessary for present purposes remain distinct and
uninjured, as follows:
III, }
Ix } 10, XI[(I)]I.
Cimi }
Judging by these and the few numbers remaining, the entire series was as
follows:
III, }
Ix }
Cimi }
Ezanab } 10, XIII; 4, IV; 20, XI; 9, VII; 9, III
Oc }
Ik }
The only doubt in reference to the restoration is whether the second and
third pairs of numerals should be as given, or 2, II, and 22, XI. If we
select the Kan column of our Table II and count from 3 Ix of the eleventh
figure column, we reach 13 Kan. If the four year series was the system
used 13 Kan might be the first day of a year, but not the first day of an
Indication. As this is the only day referred to by the XIII which could
have been the first of a year we must seek an explanation in something
else. Counting ten days from 3 Ezanab will bring us to 13 Lamat, which is
the last day (counting the five added days) of an Indication, commencing
with the year 1 Kan and ending with the year 13 Kan.
According to my theory of the ahaues,[344-1] the year 13 Kan would have
corresponded with the Gregorian years 1376, 1438, 1480, and 1532.
According to the theory advanced by Perez,[344-2] it would have
corresponded with 1385, 1437, 1489, and 1541.
It is therefore possible that this mark of distinction may be of some
value in determining the relation of the Maya to the Gregorian calendar.
FOOTNOTES:
[339-1] See Study of the Manuscript Troano, by Cyrus Thomas.
[339-2] See note on page 337.
[344-1] See Table XVII, Study of the Manuscript Troano, by Cyrus Thomas,
p. 44.
[344-2] See Table XVIII, ibid., p. 45.